Physics
GATE PH topic:quantum-mechanics PYQs
Build your understanding with focused practice from past exam papers.
Questions 71–80 of 83. Imported answers require independent review unless marked reviewed.
Question 15
Open questionPHMCQ1 markNeeds review
The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is (
is the Bohr radius)Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 31
Open questionPHMCQ2 marksNeeds review
If
is the Hamiltonian for a free particle with mass
, the commutator
isYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 47
Open questionPHNAT2 marksNeeds review
The ground state energy of a particle of mass
in an infinite potential well is
. It changes to
, when there is a small potential bump of height
and width
, as shown in the figure.
The value of
is ______ (up to two decimal places).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 50
Open questionPHNAT2 marksNeeds review
A two-state quantum system has energy eigenvalues
corresponding to the normalized states
. At time
, the system is in quantum state
. The probability that the system will be in the same state at
is ______ (up to two decimal places).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 14
Open questionPHMCQ1 markNeeds review
The wavefunction of which orbital is spherically symmetric:
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 19
Open questionPHMCQ1 markNeeds review
A one dimensional simple harmonic oscillator with Hamiltonian
is subjected to a small perturbation,
. The first order correction to the ground state energy is dependent onYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 20
Open questionPHMCQ1 markNeeds review
For the Hamiltonian
where
,
is a real vector,
is the
identity matrix, and
are the Pauli matrices, the ground state energy isYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 22
Open questionPHMCQ1 markNeeds review
The degeneracy of the third energy level of a 3-dimensional isotropic quantum harmonic oscillator is
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 23
Open questionPHMCQ1 markNeeds review
The electronic ground state energy of the Hydrogen atom is
eV. The highest possible electronic energy eigenstate has an energy equal toYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 34
Open questionPHNAT2 marksNeeds review
A free electron of energy 1 eV is incident upon a one-dimensional finite potential step of height 0.75 eV. The probability of its reflection from the barrier is ________ (up to two decimal places).
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer